Substrates of this kind have been disclosed, for example, in German Patent No. DE-38 23 642 C2. In such substrates, recesses in the form of L-shaped or meander-shaped cuts are introduced in a layer arranged on the substrate surface in order to influence the properties of the layer, for example, the resistance of the layer when the layer is a resistive film. The disadvantage of these known substrates is that the heat output densities vary as a result of the special shape of the recesses, particularly when the layer configured on the substrate is a heatable resistive film. This variation is not desirable. An analogous situation occurs when the substrate forms a resistor, and the resistor is used to measure temperature and there is a temperature distribution that varies locally. The local current density generated as a result of the distribution of the recesses causes a local variation in the weighting of the temperature field, which is generally undesirable. This is particularly disadvantageous when this type of stratified structure is a component of a precision measuring device, such as an air-mass flow meter for an internal combustion engine.